论文标题
在随机环境中进行随机分支：调查
Branching random walks in random environment: a survey
论文作者
论文摘要
我们考虑在随机适应性景观中（即随机分支/杀伤率）等离散结构等离散结构上的分支粒子过程。主要的问题是，如果州空间很大，人口主要部分位于人口的主要部分。为了回答这个问题，我们将期望与固定速率有关迁移（突变）和分支/杀戮（选择）机制的期望。这与抛物线安德森模型（具有随机电势的热方程式）密切相关，该模型在数学物理学中引起了人们的关注，因为观察到的间歇性的显着作用（小岛中溶液的质量的局部浓度）。我们在调查此效果的调查中提出了一些进步，这也与生物学启发的问题有关。
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a late time, if the state space is large. For answering this, we take the expectation with respect to the migration (mutation) and the branching/killing (selection) mechanisms, for fixed rates. This is intimately connected with the parabolic Anderson model, the heat equation with random potential, a model that is of interest in mathematical physics because of the observed prominent effect of intermittency (local concentration of the mass of the solution in small islands). We present several advances in the investigation of this effect, also related to questions inspired from biology.
